A Note on Statistical Hypothesis Testing: Probabilifying Modus Tollens Invalidates Its Force? Not True!

Area of Science:

• Statistics
• Logic
• Philosophy of Science

Background:

• The interpretation of statistical test results has been debated in relation to deductive reasoning.
• Four forms of deductive argument exist, with two valid and two invalid.
• Modus tollens (denying the consequent) is often considered the sole valid analog for statistical hypothesis testing.

Purpose of the Study:

• To address the argument that probabilistic evidence weakens modus tollens.
• To re-establish modus tollens as a valid deductive inference in statistical hypothesis testing.
• To correct flawed problem setups that question the applicability of modus tollens with probabilistic data.

Main Methods:

• Analysis of deductive reasoning forms.
• Examination of the relationship between conditional statements (p→q) and statistical hypothesis testing.
• Probabilistic evaluation of modus tollens.

Main Results:

• The argument against probabilified modus tollens is based on a flawed premise.
• Modus tollens retains its deductive force even when applied to probabilistic statistical evidence.
• The validity of modus tollens in statistical inference is reaffirmed.

Conclusions:

• Modus tollens is a valid form of deductive reasoning applicable to statistical hypothesis testing.
• Probabilistic evidence does not invalidate the logical structure of modus tollens.
• The interpretation of statistical evidence should correctly employ deductive principles like modus tollens.